Get your grill up to about 550 to 600 degrees, dome temperature. Use a raised grid if you have a Big Green Egg.

Remove the stalk carefully so as not to damage the mushroom cap or the gills. Place the caps in a large zip top bag, pour in enough Italian dressing to allow you to completely cover the caps when you seal up the bag, and then turn it over and over to coat the mushrooms. Let them marinate for 15 minutes.

Slice the onion into 4 slices that will cover the mushroom caps. Thoroughly brush both sides of each slice with olive oil.

Place the onion slices on the hot grid and grill for 3-4 minutes.

Then, carefully turn the onions over with a metal spatula. At the same time, place the mushroom caps on the hot grid, gill side down. (This is the underside of the cap, so place them on the grill the same way they grow out of the ground, gills down, rounded cap up.) Grill for 3 minutes.

Turn the mushroom caps over with the spatula. Carefully move one slice of onion to each mushroom cap. Sprinkle each mushroom/onion unit with a healthy dose of shredded cheese. Grill about another 2 minutes until the cheese is thoroughly melted.

Remove to a platter and serve.

Notes:

You can use pretty much any cheese you like. Another option besides provolone and mozzarela would be any type of bleu cheese.

You could either serve them on toasted hamburger buns or as a side dish. If you serve as a side dish, serve with sharp knives as cutting through the mushroom, onion and cheese may be a bit difficult with a common table knife.